Evaluate 2sin30+5tan60sin60 2 sin ? 30 + 5 tan ? 60 sin ? 60 , leaving your answer in surd form.

Question 1 Report

Evaluate $\frac{2 \sin 30 + 5 \tan 60}{\sin 60}$ , leaving your answer in surd form.

\frac{2 \sqrt{3}}{3} + 10

\frac{3 \sqrt{2} - 1}{5}

\frac{3 \sqrt{2} + 1}{5}

\frac{2 \sqrt{3}}{3} - 10

Answer Details

$\frac{2 \sin 30 + 5 \tan 60}{\sin 60}$
$\sin 30 = \frac{1}{2}; \tan 60 = \sqrt{3}; \sin 60 = \frac{\sqrt{3}}{2}$
$∴ \frac{2 \sin 30 + 5 \tan 60}{\sin 60} = \frac{2 (\frac{1}{2}) + 5 (\sqrt{3})}{\frac{\sqrt{3}}{2}}$
= $\frac{1 + 5 \sqrt{3}}{\frac{\sqrt{3}}{2}}$
= $\frac{2 (1 + 5 \sqrt{3})}{\sqrt{3}}$
= $\frac{2 + 10 \sqrt{3}}{\sqrt{3}}$
Rationalizing, we get
= $\frac{2 \sqrt{3} + 30}{3}$
= $\frac{2}{3} \sqrt{3} + 10$

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Logarithms

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